ewspec3: Compute evolutionary wavelet spectrum of a time series.
In locits: Test of Stationarity and Localized Autocovariance

ewspec3

R Documentation

Compute evolutionary wavelet spectrum of a time series.

Description

This function is a development of the ewspec function from wavethresh but with more features. The two new features are: the addition of running mean smoothing and autoreflection which mitigates the problems caused in ewspec which performed periodic transforms on data (time series) which were generally not periodic.

Usage

ewspec3(x, filter.number = 10, family = "DaubLeAsymm",
    UseLocalSpec = TRUE, DoSWT = TRUE, WPsmooth = TRUE,
    WPsmooth.type = "RM", binwidth = 5, verbose = FALSE,
    smooth.filter.number = 10, smooth.family = "DaubLeAsymm",
    smooth.levels = 3:WPwst$nlevels - 1, smooth.dev = madmad,
    smooth.policy = "LSuniversal", smooth.value = 0,
    smooth.by.level = FALSE, smooth.type = "soft",
    smooth.verbose = FALSE, smooth.cvtol = 0.01,
    smooth.cvnorm = l2norm, smooth.transform = I,
    smooth.inverse = I, AutoReflect = TRUE)

Arguments

`x`	The time series you want to compute the evolutionary wavelet spectrum for.
`filter.number`	Wavelet filter number underlying the analysis of the spectrum (see `filter.select` or `wd` for more details).
`family`	Wavelet family. Again, see `filter.select` or `wd` for more details.
`UseLocalSpec`	As `ewspec`, should usually leave as is.
`DoSWT`	As `ewspec`, should usually leave as is.
`WPsmooth`	If `TRUE` then smoothing is applied to the wavelet periodogram (and hence spectrum).
`WPsmooth.type`	The type of periodogram smoothing. If this argument is `"RM"` then running mean linear smoothing is used. Otherwise, wavelet shrinkage as in `ewspec` is used.
`binwidth`	If the periodogram smoothing is `"RM"` then the this argument supplies the `binwidth` or number of consecutive observations used in the running mean smooth.
`verbose`	If `TRUE` then messages are produced. If `FALSE` then they are not.
`smooth.filter.number`	If wavelet smoothing of the wavelet periodogram is used then this specifies the index number of wavelet to use, exactly as `ewspec`.
`smooth.family`	If wavelet smoothing of the wavelet periodogram is used then this specifies the family of wavelet to use, exactly as `ewspec`.
`smooth.levels`	If wavelet smoothing of the wavelet periodogram is used then this specifies the levels to smooth, exactly as `ewspec`.
`smooth.dev`	If wavelet smoothing of the wavelet periodogram is used then this specifies deviance used to compute smoothing thresholds, exactly as `ewspec`.
`smooth.policy`	If wavelet smoothing of the wavelet periodogram is used then this specifies the policy of wavelet shrinkage to use, exactly as `ewspec`.
`smooth.value`	If wavelet smoothing of the wavelet periodogram is used then this specifies the value of the smoothing parameter for some policies, exactly as `ewspec`.
`smooth.by.level`	If wavelet smoothing of the wavelet periodogram is used then this specifies whether level-by-level thresholding is applied, or one threshold is applied to all levels, exactly as `ewspec`.
`smooth.type`	If wavelet smoothing of the wavelet periodogram is used then this specifies the type of thresholding, "hard" or "soft", exactly as `ewspec`.
`smooth.verbose`	If wavelet smoothing of the wavelet periodogram is used then this specifies whether or not verbose messages are produced during the smoothing, exactly as `ewspec`.
`smooth.cvtol`	If wavelet smoothing of the wavelet periodogram is used then this specifies a tolerance for the cross-validation algorithm if it is specified in the `smooth.policy`, exactly as `ewspec`.
`smooth.cvnorm`	Ditto to the previous argument, but this one supplies the norm used by the cross-validation.
`smooth.transform`	If wavelet smoothing of the wavelet periodogram is used then this specifies whether a transform is used to transform the periodogram before smoothing, exactly as `ewspec`.
`smooth.inverse`	Should be the mathematical inverse of the `smooth.transform` argument.
`AutoReflect`	Whether the series is internally reflected before application of the wavelet transforms. So, `x` becomes `c(x, rev(x))` which is a periodic sequence. After estimation of the spectrum the second-half of the spectral estimate is junked (because it is a reflection of the first half). However, the estimate is better. This argument improves over `ewspec` where poor estimates near boundaries were obtained because the transforms assume periodicity but most time series are not (and X_1 and X_T are very different, etc).

Value

Precisely the same kind of output as ewspec.

Author(s)

Guy Nason.

References

Nason, G.P. (2013) A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series. J. R. Statist. Soc. B, 75, 879-904. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1111/rssb.12015")}

Examples

#
# Generate time series
#
x <- tvar1sim()
#
# Compute its evolutionary wavelet spectrum, with linear running mean smooth
#
x.ewspec3 <- ewspec3(x)
#
# Plot the answer, probably its a bit variable, because the default bandwidth
# is 5, which is probably inappropriate for many series
#
## Not run: plot(x.ewspec3$S)
#
# Try a larger bandwidth
#
x.ewspec3 <- ewspec3(x, binwidth=100)
#
# Plot the answer, should look a lot smoother
#
# Note, a lot of high frequency power on the right hand side of the plot,
# which is expected as process looks like AR(1) with param of -0.9
#
## Not run: plot(x.ewspec3$S)
#
# Do smoothing like ewspec (but additionally AutoReflect)
#
x.ewspec3 <- ewspec3(x, WPsmooth.type="wavelet")
#
# Plot the results
#
## Not run: plot(x.ewspec3$S)
#
# Another possibility is to use AutoBestBW which tries to find the best
# linear smooth closest to a wavelet smooth. This makes use of ewspec3
#

locits documentation built on Sept. 8, 2023, 5:07 p.m.